Generating matrix of discrete Fourier transform eigenvectors

This paper provides a novel method to obtain the eigenvectors of discrete Fourier transform (DFT), which are accurate approximations to the continuous Hermite-Gaussian functions (HGFs). The proposed method uses a generating matrix and an initial eigenvector. By multiplying the initial eigenvector with the generating matrix, we can derive a new eigenvector. Repeating this procedure we can acquire all the eigenvectors. Compare with the conventional O(N³) commutative matrix method, this new method can generate all the DFT eigenvectors with complexity reduced to O(N²logN). The generating matrix can be further used to intensify the conventional commuting matrix. The simulation result shows that the Hermite-Gaussian like (HGL) eigenvectors of the strengthened commuting matrix outperform those of Santhanam´s.